A welded steel bridge member contains a central crack of initial half-length ( )

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Fracture: stress concentration, cracks and toughness

Problem

A welded steel bridge member contains a central crack of initial half-length a0=0.5 mma_0=0.5\,\mathrm{mm} (Y=1Y=1). Passing traffic cycles its stress through a range Δσ=80 MPa\Delta\sigma=80\,\mathrm{MPa}, and at the peak stress the critical half-length is ac=25 mma_c=25\,\mathrm{mm}. The steel follows the fatigue law of Section 8.8 with CP=10−11 m cycle−1 (MPa m1/2)−3C_P=10^{-11}\,\mathrm{m\,cycle^{-1}\,(MPa\,m^{1/2})^{-3}} and m=3m=3. ((a)) Find the number of cycles to failure. ((b)) At 20002000 loading cycles a day, how many years is that?

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